cp's OEIS Frontend

A270390 Greatest common divisor of 2^n-1 and 5^n-1.

%I A270390 #19 Nov 30 2021 15:52:15
%S A270390 1,3,1,3,1,63,1,3,1,33,1,819,1,3,31,51,1,3591,1,1353,1,69,1,819,1,3,1,
%T A270390 87,1,21483,1,51,1,3,71,1727271,1,3,79,1353,1,2408301,1,6141,31,141,1,
%U A270390 13923,1,8283,1,159,1,10773,1,87,1,177,1,698476779,1,3,1,32691,1
%N A270390 Greatest common divisor of 2^n-1 and 5^n-1.
%C A270390 Ailon and Rudnick conjecture that a(n) = 1 infinitely often.
%H A270390 Antti Karttunen, <a href="/A270390/b270390.txt">Table of n, a(n) for n = 1..10000</a>
%H A270390 N. Ailon and Z. Rudnick, <a href="http://arXiv.org/abs/math/0202102">Torsion points on curves and common divisors of a^k-1 and b^k-1</a>, arXiv:math/0202102 [math.NT], 2002; Acta Arith. 113 (2004), no. 1, 31-38.
%F A270390 a(n) = gcd(2^n - 1, 5^n - 1).
%F A270390 a(n) = gcd(A000225(n), A024049(n)).
%e A270390 For n=3, 2^3-1 = 7 and 5^3-1 = 124, thus a(3) = gcd(7,124) = 1.
%p A270390 seq(igcd(2^n-1, 5^n-1), n=1..100);
%t A270390 Table[GCD[2^n - 1, 5^n - 1], {n, 100}]
%o A270390 (Sage) [gcd(2^n-1,5^n-1) for n in [1..100]]
%o A270390 (PARI) vector(100,n,gcd(2^n-1,5^n-1))
%Y A270390 Cf. A086892, A000225, A024049, A349748.
%K A270390 nonn
%O A270390 1,2
%A A270390 _Tom Edgar_, Mar 16 2016